1. Field of the Invention
The present invention relates to a method for determining a coordinate transformation between a coordinate system of a first object to be imaged by an X-ray machine and a coordinate system of a second object to be navigated relative to the first object.
2. Description of the Prior Art
xe2x80x9cNavigationxe2x80x9d of a second object relative to a first object is generally defined as guiding the second object relative to the first object, aided by optical imaging information, where an image of the second object is inserted into imaging information on the first object obtained using the X-ray machine.
This type of procedure is becoming of increasing importance, particularly in the medical field, where, in the case of navigation-guided operations, an image of a medical instrument is usually inserted into recorded imaging information on a living being. This approach allows an operator to guide an instrument that has at least partially penetrated the living being and whose tip is no longer directly visible due to, for example, its having penetrated bodily tissue. Guidance is based on imaging information relative to that area of the tissue of the living being that is to be investigated or treated, without running the risk of inadvertently injuring the living being.
In order to allow such navigation-guided operations, i.e., to be able to insert an accurately positioned and accurately oriented image of the instrument into imaging information on a living being, it is necessary to generate a mathematical relationship in the form of a coordinate transformation between a coordinate system inscribed on the living being and a coordinate system of the instrument to be navigated. To that end, artificial markings are occasionally arranged on the living being or anatomical markings, for example, prominent bone structures, are established as references. The anatomical or artificial markings must be clearly visible in X-ray images of the living being and readily accessible on the living being. These artificial markings are, for example, attached to the surface of the skin of the living being, in order to allow their registration, which is defined as determining the rule for transforming the spatial coordinates defined for the coordinate system of the instrument to be navigated into the spatial coordinates of the living being to be employed for the navigation. The markings usually have to be individually accessed by the instrument in order to be able to determine the coordinate transformation between the coordinate system of the living being and the coordinate system of the instrument. The markings also are rigidly attached to the body of the living being in the case of high-precision medical procedures. Examples are the attachment of a stereotactile framework to a patient""s head or the attachment of markings to a patient""s bones or spinal column. The markings are sometimes attached in a separate operation, since they have to be attached prior to preoperative imaging, which is frequently employed for navigation purposes.
Attachment and registration of the markings is thus a relatively unpleasant procedure for a patient, as well as a relatively time-consuming procedure for an operator handling preparations for a navigation-guided operation.
A device and a method for computer-assisted surgery are known from DE 695 03 814 T2, corresponding to U.S. Pat. No. 5,792,147. In this case a particular light pattern is projected onto a location on a patient""s body for which 3D-images have been previously obtained and archived. The light pattern is recorded by video cameras and employed for generating 3D-images of the light pattern. The archived 3D-images are superimposed on the 3D-images of the light pattern projected onto the surface of the patient""s body in order to generate a common reference frame. The cameras also record a pattern that has an indicator that is inserted into the superimposed 3D-images for navigation purposes.
German OS 196 32 273 describes methods for determining the geometric parameters of a body that is free to move.
German OS 195 36 180, corresponding to U.S. Pat. No. 5,769,861 proposes rigidly attaching to a patient""s body an internal marker fixture to establish an intracorporeal spatial reference system for localizing an instrument relative to three-dimensional data on the patient. The positions of three-dimensional data on the patient""s body obtained from an analytical scan within the intracorporeal reference system established by the marker fixture are determined in conjunction with said analytical body scan. The location and orientation of the intracorporeal reference system established by the internal marker fixture relative to an extracorporeal reference system established by an external marker fixture are determined. The location and orientation of an instrument to be navigated in relation to the external marker fixture are determined, which allows a correlation to the internal marker fixture, and thus to the three-dimensional data on the patient""s body, to be established.
A device and a method for correlating a center of intracardial activity that has been localized based on an electrocardiogram to an ultrasonic tomogram are known from German OS 43 06 037. This involves marking the location of a site of intracardial activity determined from an electrocardiogram on an ultrasonic tomogram with the aid of a position-acquisition system.
An object of the present invention to provide a method for determining a coordinate transformation between a coordinate system of a first object to be imaged by an X-ray machine and a coordinate system of a second object to be navigated relative to the first object that will eliminate the need for registration involving markings in order to define a relationship between the coordinate system of the first object and the coordinate system of the second object.
This object is inventively achieved in a method for determining a coordinate transformation between a coordinate system of a first object to be imaged by an X-ray apparatus and a coordinate system of a second object to be navigated relative to the first object, where a position-acquisition system for determining the positions of the X-ray apparatus and the second object is available, having the following method steps:
a) determining the transformation relationships L, V, and S between coordinate systems of the position-acquisition system, the X-ray apparatus, and the first object in a calibration run prior to obtaining imaging information from the first object using the X-ray apparatus, L being the coordinate transformation between a coordinate system of a marking arranged on said X-ray apparatus that interacts with the position-acquisition system and the coordinate system of the position-acquisition system, V being the coordinate transformation between the coordinate system of the position-acquisition system and the coordinate system of the first object, and S being the coordinate transformation between the coordinate system of the marking for a reference position of the X-ray apparatus relative to the first object and the coordinate system of the first object,
b) determining the modified coordinate transformation Lxe2x80x2 between the coordinate system of the marking and the coordinate system of the position-acquisition system resulting from an altered position of the X-ray apparatus and the position-acquisition system relative to one another while obtaining imaging information from the first object using the X-ray apparatus, compared to the calibration run, or determining the modified coordinate transformation LSxe2x80x2 between the coordinate system of the marking and the coordinate system of the position-acquisition system for the reference position of the X-ray apparatus relative to the first object while obtaining imaging information from the first object using the X-ray apparatus compared to the calibration run,
c) determining the coordinate transformation Lxe2x80x3 between the coordinate system of the second object and the coordinate system of the position-acquisition system, and
d) determining the coordinate transformation between the coordinate system of the second object and the coordinate system of the first object based on the coordinate transformations V, L, Lxe2x80x2, LSxe2x80x2, Lxe2x80x3, and S determined in steps a) through c).
According to the invention, a transformation relationship between the coordinate system of a first object and the coordinate system of a second object employed for navigating said second object relative to the first object is derived by determining coordinate transformations between the items of equipment involved in the imaging and the objects alone, without having to perform any registrations involving markings.
In an embodiment of the present invention an image of the second object obtained using a C-arm X-ray apparatus is inserted into a 3D-image of the first object for navigation purposes. Various 3D-images may be obtained from a series of 2D-projections taken at different projection angles of the X-ray system of said C-arm X-ray apparatus relative to the first object. Knowledge of the projection geometries involved, expressed in terms of xe2x80x9cprojection matricesxe2x80x9d determined from a single calibration procedure performed with the aid of an X-ray calibration phantom for the employed X-ray apparatus, prior to undertaking measurements on patients, is required. The coordinate transformations L, V, and S mentioned above are determined during this calibration procedure. Determining the projection matrices and determining the coordinate transformations L, V, and S is described in detail in the article by M. Mitschke and N. Navab entitled xe2x80x9cRecovering Projection Geometry: How a cheap camera can outperform an expensive stereo system,xe2x80x9d IEEE Computer Science Conference on Computer Vision and Pattern Recognition, Jun. 13-15, 2000, Hilton Head Island, S.C. Volume 1, pp. 193-200, the teachings of which are incorporated herein by reference.
Finally, the coordinate transformation between the coordinate system of the second object and the coordinate system of the first object is determined, based on the coordinate transformations L, V, and S determined from the calibration run using the coordinate transformations, Lxe2x80x2, LSxe2x80x2, and Lxe2x80x3, determined while obtaining imaging information from the first object with the position-acquisition system.
In another embodiment of the present invention a coordinate transformation M is determined from the coordinate transformations L and Lxe2x80x2 employing the relationship M=Lxe2x80x2Lxe2x88x921, which expresses the variation in the transformation relationship between the coordinate system of the marking arranged on the X-ray apparatus and the coordinate system of the position-acquisition system. This change is due to the fact that the position-acquisition system and the X-ray apparatus usually have different positions and orientations relative to one another during navigation-guided operations than during calibration. According to a variant of the present invention, the coordinate transformation between the coordinate system of the second object and the coordinate system of the first object may thus be expressed in terms of the relationship V M Lxe2x80x3.
In another embodiment of the present invention, the coordinate transformation between the coordinate system of the second object and the coordinate system of said first object are expressed in terms of the relationship S LSxe2x80x2xe2x88x921 Lxe2x80x3, where the coordinate transformation LSxe2x80x2 has been determined for the reference position of the X-ray apparatus relative to the first object during acquisition of X-ray images of the first object with the position-acquisition system.